Polyakov-loop potential of accelerated gluonic matter and subtlety in thermodynamics

We study the one-loop Polyakov-loop effective potential in pure gluonic matter under constant acceleration. We perform the computation in both the Euclidean Rindler spacetime and the optical spacetime, which are related via a conformal transformation. The results from the two formulations correspond to physically different observables, and we clarify their connection to specific components of the energy-momentum tensor. This identification resolves a discrepancy previously noted for fields on conical backgrounds. For the Polyakov-loop expectation value, we should minimize the effective potential computed in the optical metric formulation, which concludes that real acceleration strengthens deconfining properties. We also discuss analytic continuation from real to imaginary acceleration and find a perturbatively confined phase. We point out some suggestive similarities and differences between systems under imaginary acceleration and imaginary rotation.